A nonconducting cylinder having volume `2 V_(0)` is partitioned by a fixed non conducting wall in two equal part. Partition is attached with a valve. Right side of the partition is a vacuum and left part is filled with a gas having pressure and temperature `P_(0)` and `T_(0)` respectively. If valve is opened find the final pressure and temperature of the two parts.

Explanation

From the first law thermodynamics `Delta Q = Delta U + Delta W`
Since gas expands freely therefore `Delta W = 0`, Since no heat is given to gas `Delta Q = 0`
`implies Delta U = 0` and temperature remains constant
`T_(fi nal) = T_(0)`
Since the process is isothermal, therefore
`P_(0) xx V_(0) = P_(fi nal) xx 2 V_(0) implies P_(fi nal) = P_(0)//2`